Simple:
Breslev = Not Chabad.
Chabad doesn’t like any frum group who aren’t Chabad.
Therefore, by the transitive property, Chabad doesn’t like Breslev.
I’m sure it’s amplified by the fact that Breslev also practices kiruv. Before people go trying to “prove me wrong” by talking about how nice Chabad is to fried out yidden, when have you heard them speak highly of Litvaks? Or of other kiruv groups like Aish and company?
I certainly am not anti-Lubavitch; we all have our issues. But, the idea that a group MUST have done something to earn Chabad’s scorn is totally out of line.